🤖 AI Summary
This paper addresses exact identification of directed mixed graphs in simple structural causal models (SCMs) featuring both cycles and latent confounders. Due to cyclic dependencies, the graph skeleton cannot be recovered from observational data alone; moreover, latent variables invalidate standard conditional independence (CI) tests. To overcome these challenges, the authors propose a unified causal discovery framework that jointly leverages observational and interventional data. Grounded in do-separation and σ-separation, the framework integrates CI and do-CI tests and designs minimal intervention strategies. Theoretically, it establishes the first tight lower bound on the number of interventions required per experiment. Algorithmically, it introduces bounded and unbounded variants that fully recover the graph structure—under the assumption of no bidirected edges between neighbors—achieving logarithmic-factor-optimal time complexity. Empirical evaluations confirm both practical effectiveness and theoretical optimality.
📝 Abstract
We study the problem of experimental design for accurately identifying the causal graph structure of a simple structural causal model (SCM), where the underlying graph may include both cycles and bidirected edges induced by latent confounders. The presence of cycles renders it impossible to recover the graph skeleton using observational data alone, while confounding can further invalidate traditional conditional independence (CI) tests in certain scenarios. To address these challenges, we establish lower bounds on both the maximum number of variables that can be intervened upon in a single experiment and the total number of experiments required to identify all directed edges and non-adjacent bidirected edges. Leveraging both CI tests and do see tests, and accounting for $d$ separation and $σ$ separation, we develop two classes of algorithms, i.e., bounded and unbounded, that can recover all causal edges except for double adjacent bidirected edges. We further show that, up to logarithmic factors, the proposed algorithms are tight with respect to the derived lower bounds.